An unlikely alliance between tea party Republicans and Democrats in the Senate could result in relief for thousands of federal inmates imprisoned under outdated drug sentences that treated crack cocaine dealing as a far greater offense than selling powder cocaine.

But the long-awaited movement on the issue isn’t sweeping enough — or fast enough — for the Obama administration, which announced its plans to relieve crack offenders through the executive power of clemency the same day the Senate passed its bill out of committee.

The Senate bill would make the 2010 Fair Sentencing Act — which narrowed the legal disparity between crack and powder cocaine — retroactive, as well as lowering the minimum number of years drug offenders are automatically sentenced to. That means thousands of inmates hammered with lengthy sentences for dealing as little as five grams of crack under the old laws could soon qualify for release or for shorter sentences.

The bill passed the Senate Judiciary Committee on Thursday, with the support of the group’s Democrats and three Republicans — Ted Cruz of Texas, Mike Lee of Utah and Jeff Flake of Arizona, who argue that long sentences for nonviolent drug offenders are costly and unfair. More traditional Republicans such as Orrin Hatch of Utah, who served in the Senate during the heyday of harsher crack punishments, voted against the bill.

The changing politics of the issue — with red states like Texas and Kentucky leading experiments in drug sentencing reform in part to save money — means that the bill actually has a shot in the Republican-dominated House. The decades-old trend of cracking down on drug crime with longer and longer sentences is finally reversing, under the pressure of skyrocketing prison costs and growing concern about the country’s outsized inmate population. (The U.S. makes up only 5 percent of the world population but contains a quarter of its prisoners.)

But the president and his attorney general, Eric Holder, have already begun to use executive power to address the issue, and do not plan to wait on the bill to pass to provide relief for some offenders. The president said in his State of the Union speech Tuesday that he was not afraid to go it alone and use his executive power in his final term if Congress declines to act on one of his priorities.

On Thursday, Deputy Attorney General Jim Cole announced in a speech to the New York State Bar Association that the Obama administration wants the private defense bar to comb through drug cases involving nonviolent inmates who were sentenced under policies or laws that have since changed, and offer them to the president for clemency. Cole also said the U.S. Bureau of Prisons will inform prisoners that they can apply.

“We need to identify these individuals and get well-prepared petitions into the Department of Justice,” Cole said.

The deputy argued that “these older, stringent punishments, that are out of line with sentences imposed under today's laws, erode people’s confidence in our criminal justice system.”

The Justice Department program aims to help a broader pool of drug offenders than the Senate bill does.

In 2011, about 30,000 people were serving crack cocaine sentences in federal prison, more than 80 percent of them black. Only about 8,800 of these inmates would be eligible for relief under the law being considered by the Senate, according to the U.S. Sentencing Commission, because many have prior drug convictions or other factors that would make them ineligible under the bill’s criteria. Defenders will be combing through the thousands of other cases to see which might be eligible for executive clemency.

Margaret Love, a former pardon attorney for the Justice Department, called Cole’s announcement “unprecedented.” Love represents five clients who are serving life sentences for crack, and is planning on applying for clemency for all five. None of her clients would be helped by the Senate bill, should it pass, because they had prior drug convictions when they were sentenced to life.

“There’s some people that only the president could help,” said Michael Nachmanoff, the public defender for the Eastern District of Virginia, which was home to the most crack convictions of any district over the past 25 years. “The president needs to be willing to use that power.”

In December, Obama commuted the sentences of eight crack offenders, calling the system they were imprisoned under “unfair.” Most of the eight were serving life sentences. The president exercised his clemency power just 23 times in his first term, a far lower rate than President George W. Bush.

Holder, a former federal prosecutor and judge, has long been opposed to drug sentencing laws that punish the distribution of crack cocaine far more harshly than powder cocaine, and that imprisoned nonviolent offenders for years and years, burdening the prison system. Last August, he directed U.S. attorneys to no longer automatically push for mandatory minimums when prosecuting drug cases, saying that aggravating factors, such as violence, must be present to merit longer sentences.

Federal prisons account for just 200,000 of the country’s 2 million prisoners, but advocates say the push may have a ripple effect in the states, encouraging reforms there as well. Twelve states still punish crack cocaine offenders far more harshly than powder offenders.